The invention relates to the field of signal processing, and in particular to a signal processing apparatus and method that processes data captured from a sensor such as synthetic aperture radar to provide a high-resolution image.
Synthetic aperture radar (SAR) is a well known technique for imaging stationary objects. SAR is an all weather imaging radar system that provides a high-resolution image in both the range dimension and the cross range dimension. Range resolution is achieved in a well known manner by using either a high bandwidth fixed frequency transmit pulse or a frequency modulated (FM) transmit pulse. Resolution in the cross range dimension is achieved by synthesizing a large antenna aperture.
In a conventional non-synthetic aperture radar system, resolution in the cross range dimension is:
xcex4cr=Rxcex8Bxe2x80x83xe2x80x83(1)
where:
xcex4cr=cross range
R=range
xcex8B=beamwidth of the transmitted signal in radians
Therefore, to improve the cross range resolution xcex4cr, the beamwidth xcex8B must be decreased. xcex8B is defined as:
xcex8B=(kxcex)/Dxe2x80x83xe2x80x83(2)
where:
k=constant
xcex=wavelength of the transmitted signal (i.e., c/fc)
D=antenna width
c=speed of light
fc=carrier frequency
Substituting (2) into (1), one can see that for improved cross range resolution xcex4cr, the radar designer can either increase the antenna width D or decrease the wavelength xcex of the transmitted signal. However, there are clearly limits on how large the antenna width D can get (especially on an airborne platform) to achieve cross range resolution satisfactory for imaging. Similarly, the wavelength xcex can be decreased only so far before it becomes so short that the radar performance becomes degraded in foul weather conditions (e.g., rain, snow, and sleet), or the system becomes impractical because of the bandwidth requirement. SAR solves this problem by employing signal processing techniques which allow a larger antenna of width Dxe2x80x2 to be synthesized using the motion of the radar platform (e.g., an antenna mounted on an aircraft). That is, SAR achieves cross range resolution by using the motion of the vehicle carrying the radar to generate a synthesized antenna of size Dxe2x80x2 sequentially, rather than simultaneously as in the case with a real antenna of the same size.
The key to SAR is the data processing of stored reflected return data, and the amplitude weighting, phase shifting and coherently summing of the data to form the synthetic aperture radar antenna of width Dxe2x80x2. For an overview of SAR see xe2x80x9cAn Introduction to Synthetic Aperture Radarxe2x80x9d by W. M. Brown and L. J. Porcelli, IEEE Spectrum (September, 1969) pages 52-62.
An airborne SAR system is typically used to map or image a specific ground terrain (also referred to herein as a SAR scene). As an example, FIG. 1 illustrates a SAR equipped aircraft 20 flying along a flight path 22 monitoring a certain SAR scene 24. The SAR equipped aircraft 20 transmits a series of RF pulses towards the SAR scene 24 and receives backscattered RF energy whose information content is indicative of the terrain and other reflecting objects on the terrain (e.g., buildings, trucks, cars, ships, planes . . . ). A short time later, the aircraft 20 is located at a second location 28 along the flight path 22 and again transmits RF energy towards the SAR scene 24. As known, the distance traveled by the aircraft between pulse transmissions should be less than one-half the illuminating aperture size when the radar""s line of sight is perpendicular to the platforms velocity vector. The received RF energy at the second location 28 is again indicative of the SAR scene, but this time it is taken from a different view. Since radar signals travel at the speed of light, it is known precisely when a return signal is likely to come from SAR scene 24 at a given range from the aircraft 20. Accordingly, for each transmitted RF pulse there will be a plurality of return signals corresponding to the various scatterers within the SAR scene located at various ranges from the aircraft. These returns can be processed in real-time or off-line to create an image of the SAR scene 24 and stationary objects therein using the Doppler history of the objects. That is, each return signal contains the radar carrier frequency signal fc component with a Doppler shift in frequency (fc fd), which in reality is the phase of the backscattered signal as a function of time with respect to the phase of the transmitted signal.
Referring to FIG. 2, an SAR system 30 includes an antenna 32 that transmits pulsed RF energy (e.g., X or Ku band) and receives backscattered RF energy from the illuminated SAR scene 24 (FIG. 1). The radar system 30 includes an exciter 34 and an amplifier 36 which generate and provide an uncompressed pulse of RF energy signal on a line 38 that is coupled to the antenna 32.
To obtain fine range resolution, a linear FM waveform is used in which frequency value fc is changed linearly from a frequency value f1 to a value f2 over the transmitted pulse length xcfx84. This allows the radar to utilize a long pulse to achieve a large amount of radiated energy while retaining the range resolution associated with a shorter pulse. Other known pulse compression techniques include nonlinear FM, discrete frequency shift, polyphase codes, phase coded pulse compression, compound Barker codes, coding sequences, complementary codes, pulse burst and stretch.
During receive mode, each antenna 32 receives backscattered RF energy data indicative of the SAR scene 24 (FIG. 1) being imaged and provides a received signal on a line 42 to a receiver 44. The receiver 44 coherently processes the received signal data and provides a received signal on a line 46 containing both in-phase(I) and quadrature(Q) data to a signal processor 48 A coherent reference signal is generally required for the signal processing since an azimuth angle measurement is a measurement of phase from spatially separate positions. That is, the coherent radar remembers the phase difference from transmission of a pulse to reception of the backscattered energy from the pulse. The received signals contain the carrier signal fc with a Doppler shift fd in frequency, which in reality is its phase versus time.
Each backscattered RF signal is often converted to a digital signal format as early as possible in the signal processing sequence due to the greater degree of design flexibility inherent in the discrete time domain. This often occurs after the RF received signal has been bandshifted to an intermediate frequency (IF) and then to a video signal having both an in-phase(I) and quadrature(Q) component. The sampling rate of the analog-to-digital converter (ADC) (not shown) must be fast enough to meet the well-known Nyquist sampling criteria to prevent aliasing. Once sampled and digitized, the received video signal containing the I and Q signal components can be processed by the signal processor 48 to image objects within the SAR scene. A radar processor/controller 50 controls the operation of the radar system based upon inputs received from an operator control panel/interface 52 and the current operating condition of the radar system. Images formed by the signal processor are presented on a display 54. The system also includes a memory storage 56 wherein received data can be stored for subsequent, non-realtime processing.
FIG. 3 illustrates a top-level functional block diagram of signal processing routines 60 performed either in real-time or off-line to image stationary object within the SAR scene 24 (FIG. 1). To implement the routines in real-time, one skilled in the art will appreciate that the signal processor 48 requires a large amount of data storage and processing power.
The signal processor 48 executes a data calibration routine 62 that receives the digitized in-phase(I) and quadrature(Q) signals on the line 46 from the receiver 46 (FIG. 2) to correct for any front-end hardware inaccuracies. The processing steps may include subroutines to: i) remove the DC biases of the channel""s ADC; ii) ensure that the in-phase(I) and quadrature(Q) components of the signal are in true quadrature; iii) balance the I-Q gains and correct for receive chain mismatches including time alignment; and iv) gain and phase versus frequency alignment. The data calibration routine also includes a pulse compression subroutine that provides compressed data in a well known manner in the frequency versus time domain. Pulse compression techniques used to increase the total RF energy while maintaining high range resolution are well known. Once complete, the data calibration routine 62 provides calibrated received signals on a line 64. In general, the data calibration routine 62 may include as many hardware receiver chain error corrections as necessary to reduce the amount of error introduced by the receiver 44 to an acceptable systems level. The next processing step is to motion compensate the calibrated received signals on line 64.
As known, the motion compensation routine compensates for the aircraft motion with respect to the SAR scene 24 (FIG. 1). Because the aircraft is not flying along a straight line or at a constant velocity, the backscattered energy experiences a frequency shift and time delay, both as a function of time, which must be corrected to provide a coherent phase history of the stationary objects during the dwell time. The dwell time as used herein is the period of time over which the radar system illuminates an area and generally is about 0.1 second to about 10 seconds, or more. These corrections are required in a high resolution SAR in order to keep the individual scattering elements on a reflecting target coherent over the dwell period and at squint angles other than 90xc2x0. In general, motion compensation is well known and involves electronically adjusting the phase of the received signals on the line 64. Ideally, the processed synthetic aperture information is completely isolated from the effects of undesired aircraft motion during the dwell time.
The distance the aperture has moved pulse-to-pulse is typically calculated based upon information obtained from an inertial navigation system (INS), an inertial measurement unit (IMU), and/or a global positioning system (GPS) (all not shown). The position measurement signals are provided on a line 68 and the motion compensation routine computes a correction signal value that represents the amount of time delay to be applied to the calibrated received signals on the line 64 to provide motion compensated received signals on a line 70. A new time delay (i.e., a time shift) is applied for each pulse or synthesized pulse, if multiple pulses are used to achieve the desired bandwidth using pulse compression techniques. The following papers discuss motion compensation and the details of performing the same: xe2x80x9cMotion Compensation for Synthetic Aperture Radarxe2x80x9d by J. C. Kirk, Jr, IEEE Transaction on Aerospace and Electronic Systems, Vol. AES-11, No. 3 (May 1975); xe2x80x9cSynthetic Aperture Imaging With Maneuversxe2x80x9d by J. H. Minns and J. L. Farrell,); IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-8, No. 4 (July 1972); and xe2x80x9cEffects of Navigation Errors in Maneuvering SARxe2x80x9d, by J. L. Farrell, J. H. Minns and A. Sorrell, IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-9, No. 5 (September 1973).
The next processing step is performed by a presum routine 72 of the motion compensated received signal on the line 70 to create signal information that can be processed to form the image. Presuming reduces the computational burden of SAR processing by narrow band filtering the azimuth samples (pulses) and reducing the sampling rate. This filtering may be performed by weighting the received signals on the line 70. Presumming is well known and discussed in xe2x80x9cSynthetic Aperture Processing With Limited Storage and Presummingxe2x80x9d by W. M. Brown, G. G. Houser and R. E. Jenkins; IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-9, No. 2 (March 1973). Also see xe2x80x9cA Discussion of Digital Signal Processing in Synthetic Aperture Radarxe2x80x9d by J. C. Kirk, Jr., IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-11, No. 3 (May 1975). In general, presumming is used to reduce the amount of data that is stored in main memory since the Doppler bandwidth of the system may be larger than what is actually necessary to image the stationary objects in the SAR scene 24 (FIG. 1). Therefore, only the Doppler band associated with stationary objects is retained for further processing.
Next, a polar reformat routine 76 receives pre-summed data on a line 74 to correct for the distortion of the scatterer""s (i.e., an RF reflective surface) position about the center of the SAR scene (often referred to as the map center). A block of reformatted data is provided on a line 78 to subroutine 80 which corrects the reformatted data for fine range slip error which occurs due to the fact the INS is not infinitely accurate. The fine range slip correction value is adaptively computed by the subroutine and applied to prevent range walk by placing all the energy from the same scatter in the same range resolution cell. Range walk is the result of the stationary object xe2x80x9cwalkingxe2x80x9d through one or more range resolution cells during the dwell time. The fine range slip correction subroutine 80 then provides a corrected signal on a line 82 to an autofocus subroutine 84 that focuses the image of the stationary objects in the SAR scene. Subroutine 86 then forms the image of the stationary objects in the SAR scene that is enhanced by a brightness transfer subroutine (BTF) 88 that provides a SAR image signal on a line 90. The SAR image signal contains displayable quality images of the stationary objects (i.e., buildings, terrain and parked vehicles) in the SAR scene.
In conventional SAR processing the image is generally formed using a two dimensional Fast Fourier Transform (i.e., a 2-D FFT). One drawback, however, to using the FFT is inherent limitations on resolving more than one scatterer within a resolution cell. The ability to resolve scatterers is limited by the number of data samples available. Further, the undesirable side effect of side lobes that result from performing the FFT on a finite number of data samples can also affect the ability to the resolve of scatterers. Typically, it is sought to suppress these side lobes. One technique that has been used to reduce the presence of side lobes is the windowing of the data signal before performing the FFT. This, however, increases the main lobe width, which further reduces the ability to resolve closely spaced scatterers. Thus, a problem with conventional SAR processing is the difficultly of resolving more than one scatterer within a resolution cell.
There has, therefore, been research into a number of so-called superresolution techniques for forming images. These are called superresolution because they resolve beyond the inherent Fourier resolution limits of the data. The minimum variance techniques derived from Capon""s minimum-variance technique (called MLM, or Maximum Likelihood Method) are one such group of superresolution techniques. Minimum variance techniques entail the derivation of a unique set of weighting coefficients to estimate the radar cross section (RCS), or energy density, at each output pixel. The weighting coefficients replace the FFT used in conventional SAR image formation. Essentially, these techniques seek to minimize the power from additive noise (which is known to be given by its covariance), while keeping unit gain for the signals sought. That is,
I(r,c)=minxcfx89HRxcfx89xe2x80x83xe2x80x83(3)
such that
xcfx89Hv(r,c)=1,
where I(r,c) is the output image at location range r and cross-range c, xcfx89 is a vector of the weighting coefficients (i.e., beam forming or combining coefficients) which are applied to the covariance matrix R (also known as the autocorrelation matrix) of the data, and v(r,c) is the steering vector for a point scatterer at the location (r,c). A steering vector, v(r,c), is an idealized point scatterer response. That is, if an ideal point scatterer is located at only one of the pixels, then a response is provided that is the steering vector for that scatterer within a scaling factor and an overall phase constant. H is the complex conjugate transpose (also referred to as a Hermetian). R=xxH, where x is a vector of the data samples.
As described, the additive noise sought to be minimized is given by its covariance. Therefore, the accuracy of any minimum-variance algorithm depends on the accuracy of the covariance estimate. Further, many minimum-variance techniques require a full rank covariance matrix. With only one phase history observation, however, the covariance matrix is rank deficient. Therefore, in most specific cases, the covariance estimate of the data samples is improved by using multiple looks. Looks are different realizations of the same data. In this case,   R  =            1      K        ⁢                  ∑                  k          =          1                K            ⁢                        x          k                ⁢                  x          k          H                    
where xk is a look vector.
As shown in equation (3), a minimum-variance technique computes a solution for xcfx89 that minimizes the power, or energy, or RCS at this one given pixel of interest for a given model. That is, the output image at one given pixel (i.e., r, c) is computed by using weights xcfx89 that minimize the product xcfx89HRxcfx89.
One solution that minimizes xcfx89HRxcfx89 is xcfx89=0. However, this is an unacceptable solution since there would be no image left. Therefore, possible solutions must be further constrained. Therefore, what generally differentiates various minimum variance techniques are the constraints imposed and/or assumptions made about the covariance matrix.
One constrained minimum variance technique is the so-called High-Definition Vector Imaging (HDVI), which is describe in U.S. patent application Ser. No. 09/025,994, entitled xe2x80x9cHigh-Definition Imaging Apparatus and Method,xe2x80x9d and filed on Feb. 19, 1998, incorporated herein by reference. In HDVI, the weights xcfx89 are further constrained in norm ∥xcfx89∥xe2x89xa6xcex2 to reduce the loss of sensitivity to bright scatters. The weights xcfx89 are also constrained to a particular subspace in order to preserve background information in the image. This constraint is accomplished by confining the selection of the weighting vector xcfx89 to the subspace defined by the linear space of the columns of the covariance matrix generated from the data. HDVI provides dramatic sidelobe cancellation along with significantly improved resolution (i.e., narrower main lobes).
Unfortunately, even though improvements in image quality for human exploitation with HDVI are evident, they have not been implemented due to the computational cost. The computational cost of HDVI, specifically the constrained-weight minimum-variance technique is approximately 8000 real operations (e.g., one real-valued multiply-and-accumulate is counted as two operations) per input pixel. The resultant image is upsampled by a factor of two, in both range and cross-range, to account for the narrower point response. The major computational burdens are the generation of the covariance matrix (frequency-domain autocorrelation), the eigen-decomposition of this matrix, and the imaging of the resultant eigenvectors for every output pixel.
There is therefore a need for a minimum variance technique for sensor data processing that provides the benefits of HDVI at a reduced computational burden.
In one aspect of the present invention, a method of processing image data to produce a high-definition image is provided. The image data is received and adaptively processed using a constrained minimum variance method to iteratively compute the high-definition image. The high-definition image I is expressed in range and cross-range as I(r,c)=minxcfx89HRxcfx89, where xcfx89 is a weighting vector and R is a covariance matrix of the image data. A solution for I(r,c) is approximated by i) forming Y=[x1 . . . xK]T/{square root over (K)}, where x1 . . . xk are beamspace looks formed from image domain looks and with y1, y2, and y3 denoting the Kxc3x971 columns of Y; ii) computing r21=y2Ty1 and r31=y3Ty1, and b=r21y2+r31y3; computing xcex3 as       γ    =          min      ⁡              (                                                            r                21                2                            +                              r                31                2                                                                    b                T                            ⁢              b                                ,                                                    β                -                1                                                              r                  21                  2                                +                                  r                  31                  2                                                                    )              ;
and iii) computing I(r,c) as I(r,c)=∥y1xe2x88x92xcex3b∥2.
In another aspect of the present invention, a system for processing image data to produce a high-definition image is provided. The system includes a preprocessing routine, a make beamspace looks routine, and a minimum variance method routine. The peprocessing routine receives the image data and generates a plurality of image domain looks. The make beamspace looks routine then generates k beamspace looks, x1 . . . xk, from the plurality of image domain looks. The minimum variance method routine then iteratively computes the high-definition image from the beamspace looks, wherein the high-definition image I is expressed in range and cross-range as I(r,c)=minxcfx89HRxcfx89, where xcfx89 is a weighting vector and R is a covariance matrix of the image data. The minimum variance method routine approximates a solution for I(r,c) by i) forming Y=[x1 . . . xK]T/{square root over (K)} with y1, y2, and y3 denoting the Kxc3x971 columns of Y; ii) computing r21=y2Ty1 and r31=y3Ty1, and b=r21y2+r31y3; computing xcex3 as       γ    =          min      ⁡              (                                                            r                21                2                            +                              r                31                2                                                                    b                T                            ⁢              b                                ,                                                    β                -                1                                                              r                  21                  2                                +                                  r                  31                  2                                                                    )              ;
and iii) computing I(r,c) as I(r,c)=∥y1xe2x88x92xcex3b∥2.
In another aspect of the present invention, the high-definition image is combined with unweighted and Taylor-weighted images to provide a more detailed image.
These and other features and advantages of the present invention will become apparent in light of the following detailed description and accompanying drawings.